- Normal Distribution

The probability density function of a normal random variable X with mean µ and standard deviation σ is given by

f(x|µ, σ) = 1 σ √ 2π

exp

[ − (x− µ)

2σ2

] ,−∞ < x <∞, −∞ < µ <∞, σ > 0.

This distribution is commonly denoted by N(µ, σ2). The cumulative distribution function (cdf) is given by

F (x|µ, σ) = ∫ x −∞

f(t|µ, σ)dt.